In this section, we validate our approach using two synthetic problems and a (more) realistic engineering application to quantify the extreme ship motion probability in irregular waves. For all cases, we present the results from our current method of sequential sampling (or sequential BED) with VHGPR as a surrogate model (Seq-VHGPR), as well as other methods for validation and comparison. These other methods include Monte Carlo sampling using one million samples for accurate estimation of the mean and variance of ItR (Exact-MC, which serves as the exact result to validate Seq-VHGPR);
space-filling Latin hypercube (LH) sampling [1]} with VHGPR as a surrogate (LH-VHGPR, which serves as a reference to demonstrate the efficiency of sequential sampling); LH sampling with SGPR as a surrogate (LH-SGPR, to demonstrate the necessity of using VHGPR). We remark that the asymptotic LH-SGPR solution (with increase of sampling number) corresponds to the best solution that can be achieved by previous vast methods using SGPR [2]}, [3]}, [4]}, [5]}.
